Adjusted means (concluded): The notion of an adjusted mean was discussed in Exercises 7.2, 7.3, and 8.6. Now consider the ANCOVA model for two factors, R and C, and two covariates, X1
and X2:
Note that this formulation of the model permits interactions between the factors but not between the factors and the covariates.
(a) How can the ANCOVA model be used to compute adjusted cell means for the r · c combinations of levels of the factors R and C?
(b) In computing adjusted means, is anything gained by expressing the covariates as deviations from their respective means rather than as raw scores?
(c) If the interactions between the factors γjk
are deleted from the model, how can we calculate adjusted means for the r categories of R and the c categories of C?
The calculation of adjusted means in additive ANCOVA models is a traditional use of the ANCOVA. Further information on adjusted means can be found in Searle, Speed, and Milliken (1980). Adjusted means are special cases of effect displays, as developed in this and the preceding chapter.